What is a equation of a line that passes threw the points (3,1) and (-2,4)

The ratio of the vertical rise to the horizontal distance on the ramp is equal to tan B.

The given figure represents a ramp with a length of 17 feet, rising 8 feet above the floor, and covering a horizontal distance of 15 feet. To find the ratio of the vertical rise to the horizontal distance (tan B), we can use the trigonometric function tangent (tan).

Tan B = vertical rise / horizontal distance = 8 feet / 15 feet = 0.5333

Equation for line: y=mx+b where m is the slope and b is the y-intercept

We have the slope. We just need to find the y-intercept. Plug in the point and the slope and solve for b.

y=mx+b

1=4(-5)+b

b=21

Answer: y=4x+21

Answer:

x=-5, x=9

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2} -8x-90[/tex]  

equate to zero

[tex]2x^{2} -8x-90=0[/tex]  

so

[tex]2=-1\\b=-8\\c=-90[/tex]

substitute in the formula

[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{784}} {4}[/tex]

[tex]x=\frac{8\pm28} {4}[/tex]

[tex]x=\frac{8+28} {4}=9[/tex]

[tex]x=\frac{8-28} {4}=-5[/tex]

therefore

The solutions are x=-5, x=9

For this case we must simplify the following expression:

[tex]\frac {1} {2} (6 \frac {2} {3} + \frac {1} {4}) - \frac {5} {24} =[/tex]

We convert the mixed number to an improper fraction:

[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]

So, by rewriting we have:

[tex]\frac {1} {2} (\frac {20} {3} + \frac {1} {4}) - \frac {5} {24} =\\\frac {1} {2} (\frac {4 * 20 + 3 * 1} {4 * 3}) - \frac {5} {24} =\\\frac {1} {2} (\frac {80 + 3} {12}) - \frac {5} {24} =\\\frac {1} {2} (\frac {83} {12}) - \frac {5} {24} =[/tex]

[tex]\frac {83} {24} - \frac {5} {24} =\\\frac {83-5} {24} =\\\frac {78} {24} =\\\frac {39} {12} =\\\frac {13} {4} =\\3 \frac {1} {4}[/tex]

Answer:

[tex]3 \frac {1} {4}[/tex]

Answer:

She traveled 13 23/56 miles on the third day.

Step-by-step explanation:

HOPE THIS HELPED ;3

Answer:

Equation of line is given by:

[tex]y=2x+14[/tex]  

Step-by-step explanation:

Given points:

[tex](-8,-2)\ and\ (-4,6)[/tex]

Slope of line [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]  is a point on the line

[tex]m=\frac{6-(-2)}{-4-(-8)}[/tex]

[tex]m=\frac{6+2}{-4+8}[/tex]

[tex]m=\frac{8}{4}[/tex]

∴ [tex]m=2[/tex]

Point-slope equation of line is given by:

[tex]y-y_1=m(x-x_1)[/tex]  

where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is slope of line.

Using point [tex](-8,-2)[/tex] and slope [tex]m=2[/tex] point-slope equation of line is given by:

[tex]y-(-2)=2(x-(-8))[/tex]  

Simplifying.

[tex]y+2=2(x+8)[/tex]  

Using distribution.

[tex]y+2=2x+16[/tex]  

Subtracting 2 to both sides.

[tex]y+2-2=2x+16-2[/tex]  

[tex]y=2x+14[/tex]  

Thus, equation of line is [tex]y=2x+14[/tex]  

The probability of drawing a red marble out of the bag without looking is 1/3.

The probability of drawing a red marble out of the bag without looking can be calculated by dividing the number of red marbles by the total number of marbles in the bag. In this case, there are 3 red marbles out of a total of 9 marbles, so the probability is 3/9, which simplifies to 1/3.

Answer:

$114

Step-by-step explanation:

Sales price = Original Cost - $35

Sales price - $35 = Original Cost

Substitute in known values

$149 - $35 = Original Cost

$114 = Original Cost

Hope this helps :)

Answer:

82

Step-by-step explanation:

Mean of a set of data is simply the average. It's calculated by adding up all the numbers, then divide by how many numbers there are.

57 + 59 + 64 + 72 + 76 + 77 + 77 + 78 + 85 + 87 + 88 + 88 + 88 + 92 + 94 + 96 + 98 + 100 = 1,476

1476/18 = 82

Therefore 82 is the mean of the set of numbers

Answer:

Median = 86

Step-by-step explanation:

the middle of the data set is 85 and 87. to find the median you would do 85+87/2= 172/2 median = 86

Answer:

4

Step-by-step explanation:

3.6m = 14.4

m = 14.4 ÷ 3.6

m = 4

Answer:

Step-by-step explanation

But the question does not say exactly what should be solve for.

Answer:

A

Step-by-step explanation:

Given sequence [tex]-8,\ -1,\ 6,\ ...[/tex]

In this sequence,

[tex]a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...[/tex]

Hence,

[tex]d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7[/tex]

Find 56th term:

[tex]a_{n}=a_1+(n-1)\cdot d\\ \\a_{56}=-8+(56-1)\cdot 7\\ \\a_{56}=-8+385\\ \\a_{56}=377[/tex]

The sum of 56 terms is

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_{56}=\dfrac{-8+377}{2}\cdot 56=\dfrac{369}{2}\cdot 56=369\cdot 28=10,332[/tex]

Answer:

Step-by-step explanation:

g(h(x))=g(3x + 7). Since h(x)=3x + 7

g(h(x))= 2(3x + 7) - 5

g(h(x))= 6x + 14 -5

=6x +9

Answer:

[tex]m\angle KLM=53.13^o[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle KOM

In the triangle KOM

we have

[tex]KO=MO=r=5\ units[/tex]

[tex]KM=8\ units[/tex]

Applying the law of cosines

[tex]8^2=5^2+5^2-2(5)(5)cos(KOM)[/tex]

[tex]64=50-50cos(KOM)[/tex]

[tex]50cos(KOM)=50-64[/tex]

[tex]50cos(KOM)=-14[/tex]

[tex]cos(KOM)=-14/50[/tex]

[tex]m\angle KOM=cos^{-1}(-14/50)[/tex]

[tex]m\angle KOM=106.26^o[/tex]

step 2

Find the measure of the arc KM

we know that

[tex]arc\ KM=m\angle KOM[/tex] ----> by central angle

we have

[tex]m\angle KOM=106.26^o[/tex]

so

[tex]arc\ KM=106.26^o[/tex]

step 3

Find the measure of angle KLM

we know that

The inscribed angle is half that of the arc comprising  

[tex]m\angle KLM=\frac{1}{2}[arc\ KM][/tex]

we have

[tex]arc\ KM=106.26^o[/tex]

substitute

[tex]m\angle KLM=\frac{1}{2}[106.26^o][/tex]

[tex]m\angle KLM=53.13^o[/tex]

Answer:

[tex]x\sqrt{7} - 49\sqrt{x}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}\sqrt{7x}(\sqrt{x} - 7\sqrt{7}) & = & \sqrt{7x}\times\sqrt{x}- 7\sqrt{7}\times\sqrt{7x} \\ & = & \sqrt{7}\times\sqrt{x}\times\sqrt{x} - 7\sqrt{7}\times\sqrt{7}\times\sqrt{x}\\& = & \sqrt{7}\times x - 7\times 7\times\sqrt{x}\\& = &\mathbf{ x\sqrt{7} - 49\sqrt{x}}\\\end{array}[/tex]

Answer:

The fractions [tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex] are not in order from least to greatest.

Step-by-step explanation:

Given order of fractions from least to greatest:

[tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex]

To check if the fractions are in correct order.

Solution:

The fractions given have same numerators but different denominators.

For fractions the higher the denominator the lower is the value of that fraction.

Thus, in the given list the least value fraction will be the fraction with the greatest denominator which is [tex]\frac{3}{12}[/tex] and the greatest value fraction will be the fraction with the least denominator which is [tex]\frac{3}{9}[/tex]

So, the order of the fractions from least to greatest is not correct. Instead the order is from greatest to least.

The correct order from least to greatest should be:

[tex]\frac{3}{12},\frac{3}{11},\frac{3}{10},\frac{3}{9}[/tex].

Answer: Robert has 22 video games.

Step-by-step explanation:

Let be "r" the number of video games that Robert has and "s" the the number of video games that Samuel has.

Set up a system of equations:

[tex]\left \{ {{r=5s+7} \atop {r+s=25}} \right.[/tex]

You can use the substitution method to solve the system:

- You need to substitute the first equation into the second equation and solve for "s":

[tex](5s+7)+s=25\\\\6s=25-7\\\\s=\frac{18}{6}\\\\s=3[/tex]

- Finally you must substitute the value of "s" into the first equation and evaluate:

[tex]r=5(3)+7\\\\r=22[/tex]

Answer:3

Step-by-step explanation:

5x+7=25

So lets subtract 7 from 25 to get 5x alone...

5x=18

5x/5=x

18/5=3.3

You cant have 0.3 of a video game so the answer is 3

Answer:

The difference is [tex]\frac{3}{4}[/tex] inches.

Step-by-step explanation:

See the attached number line where the worm lengths in inches are plotted.

From the number line plotted in the attached photo, it is clear that the shortest worm has the length of [tex]\frac{3}{4}[/tex] inches and the longest worm has the length of [tex]1\frac{1}{2}[/tex] inches i.e. [tex]\frac{3}{2}[/tex] inches.

Therefore, the difference in length between the shortest and longest worm is [tex](\frac{3}{2} - \frac{3}{4}) = \frac{3}{4}[/tex] inches. (Answer)

Answer:

2 1/2 or 2.5

Step-by-step explanation:

The area is the length times the width. To solve for the length, you have this equation using the data you already have. 8 1/2 = 3 2/5 x length. 8 1/2 / 3 2/5 = length. 8.5/3.4 = length. length = 2.5 OR to do this fraction wise, you can make them fractions and divide, making 8/1 -> 16/2 + 1/2 = 17/2 and 3/1 - 15/5 + 2/5 = 17/5 and divide those, which ends up at 2 1/2 but fraction wise makes it more complicated

Answer:

if f(x)=24

24=-12x+72

24-72=-12x

-48=-12x

x=48/12

x=4

so it's (C)

Answer:

x=4; Option C is your answer.

Step-by-step explanation:

Plug in 24:

[tex]f(x)=24\\[/tex]

[tex]24=-12x+72[/tex]

Solve For X:

[tex]-12x+72-72=24-72\\-12x=-48\\\frac{-12x}{-12} =\frac{-48}{-12}\\ x=4[/tex]

Answer:

The actual distance is 127 miles.

Step-by-step explanation:

Given:

On a map, the distance from Los Angeles to San Diego is 6.35 cm.

The scale is 1 cm = 20 miles.

Now, to find the actual distance.

Let the actual distance be [tex]x\ miles.[/tex]

And the distance on map is 6.35 cm.

So, 6.35 cm is equivalent to [tex]x\ miles.[/tex]

And as given on the scale 1 cm is equivalent to 20 miles.

Now, to get the actual distance by using cross multiplication method:

[tex]\frac{6.35}{x} =\frac{1}{20}[/tex]

By using cross multiplication we get:

⇒  [tex]127=x[/tex]

⇒  [tex]x=127\ miles.[/tex]

Therefore, the actual distance is 127 miles.

The other answer is wrong the following is the sample response.

Answer:

Sample Response: The population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors.

Step-by-step explanation:

just finished the assignment and this was the sample response.

(please mark brainliest)

Have a great day!

Alan's survey population encompasses all students at the high school with art preferences. A sample could be randomly chosen from students from each grade or art class, reflecting the school's diversity and maintained by a random sampling method for fairness and representation.

The population of Alan's survey is all the students at the town’s high school who have preferences for types of art. To conduct his survey, Alan needs to choose a sample, which is a smaller group from the population that can provide reliable information about the entire population's art preferences. An example of a possible sample would be selecting a certain number of students from each grade level or art class to ensure a variety of perspectives. It could also involve stratification by demographic characteristics such as age, gender, socioeconomic status, or ethnicity if these factors are believed to influence art preferences.

An efficient method to create a representative sample could be to use a random sampling technique where each student has an equal chance of being selected. For instance, Alan could use a random number generator to pick students from a list, or he might use a stratified random sampling by first dividing the student body into subgroups (such as by grade or art class) and then randomly selecting students from each subgroup.

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Let us take 'a' in the place of 'y' so the equation becomes

(y+x) (ax+b)

Step-by-step explanation:

Step 1:

(a + x) (ax + b)

Step 2: Proof

Checking polynomial identity.

(ax+b )(x+a) = FOIL

(ax+b)(x+a)

ax^2+a^2x is the First Term in the FOIL

ax^2 + a^2x + bx + ab

(ax+b)(x+a)+bx+ab is the Second Term in the FOIL

Add both expressions together from First and Second Term  

= ax^2 + a^2x + bx + ab

Step 3: Proof

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

Identity is Found .

Trying with numbers now

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)

((10)+8)(7) =(2*25)+(4*5)+(40)+(16)

(18)(7) =(50)+(20)+(56)

126 =126

By completing the square, the equation x²- 20x + 100 = 0, we get, (x-10)²=0

Here, we have,

To rewrite the equation x² - 20x + 100 = 0 by completing the square, we can follow these steps:

Step 1: Move the constant term to the right side of the equation:

x² - 20x = -100.

Step 2: Take half of the coefficient of the x-term (-20/2 = -10) and square it to get (-10)² = 100.

Step 3: Add the result from step 2 to both sides of the equation:

x² - 20x + 100 = -100 + 100.

Simplifying:

x² - 20x + 100 = 0.

Step 4: Factor the left side of the equation. In this case, the left side is a perfect square trinomial:

(x - 10)² = 0.

Therefore, by completing the square, the equation x²- 20x + 100 = 0,

we get, (x-10)²=0

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Final answer:

The equation [tex]x^2 - 20x + 100 = 0[/tex] is already a perfect square and does not need to be completed. However, completing the square involves moving the constant to the other side, squaring half the coefficient of x, and solving for x, which leads us back to the original equation [tex](x - 10)^2 = 0[/tex] and reveals that x = 10.

Explanation:

The equation given is [tex]x^2 - 20x + 100 = 0[/tex]. This equation appears to already be a perfect square, as the constant term (100) is the square of half the coefficient of the x term (which is 10), thus completing the square is actually not needed. However, to illustrate the method of completing the square, let's ignore for a moment that it's already a perfect square and proceed with the steps:

We've found that x = 10 is the solution to the equation, which is the same result you would get by recognizing the equation was already a perfect square in its original form.

Answer:

30%

Step-by-step explanation:

We can translate the question into an equation.

500x=150

x=150/500

x=3/10=30%

answer: 30%

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]

In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.

coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.

Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].

Each point listed is of the form (x,y). The x coordinate is always listed first. We dont have any repeat x values, so this is enough to conclude we have a function.

If you wanted to, you could graph each point given on the same coordinate grid. Note how none of the points stack on top of each other. Or put another way, note how it is impossible to draw a single straight line through more than one point graphed. This graph passes the vertical line test.

A function is where plugging in any x value leads to exactly one y value.

If you had two points like (5,2) and (5,7) then the input x = 5 leads to more than one output y = 2 and y = 7 at the same time, making this example not a function.

Answer:

0.60

Step-by-step explanation:

Again, we have a 10x10 space, which means there are 100 squares.

In this case, there are 60 shaded squares. This gives the probability of [tex]\frac{60}{100}[/tex] which simplifies to 0.60

Answer:

0.60

Step-by-step explanation:

Because there are 100 squares and 60 out of it is shaded if you chose a random point amongst these 100 square the probability of choosing a shaded one is 60/100 which is equal to 0.60.

Answer:

7.2

Step-by-step explanation:

You divide 225 by 30 and get 7.2

Answer:

c

Step-by-step explanation: